Question

if α and β are the zeroes of 3x^2+6x+9 then find the value of (alpha + beta)^3 - 3alpha beta /(alpha^2+beta^2)(alpha beta)​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given -

• α and β are zeroes of polynomial p(x) = 3x² + 6x + 9

To Find -

• Value of (α + β)³ - 3αβ/(α² + β)²(αβ)

Now,

As we know that :-

• αβ = c/a

→ αβ = 9/3

→ αβ = 3

And

• α + β = -b/a

→ α + β = -6/3

→ α + β = -2

Squaring both sides :-

→ (α + β)² = (-2)²

→ α² + β² = 4 - 2αβ

→ α² + β² = 4 - 2(3)

→ α² + β² = 4 - 6

→ α² + β² = -2

Now,

The value of (α + β)³ - 3αβ/(α² + β)²(αβ) is

→ (-2)³ - 3(3)/(-2)(3)

→ -8 - 9/-6

→ -17/-6

→ 17/6

Hence,

The value of (α + β)³ - 3αβ/(α² + β²)(αβ) is 17/6.